Question

If alpha and beta are zeroes of the polynomial x^2+4x-1, then find (attached pic )​

Answer 1

Answer:

alpha + beta = -b/a

=-4/1

= -4

alpha * beta = c/a

=-1

According to the problem

=-4-1

=-5

alpha+beta + alpha*beta

=-5

Answer 2

Hi there!!

Look at the attachment for first part..

2) Alpha = A & Beta = B

= [ ( A² + B² ) / ( AB )² ] + 2( AB )³

Using a² + b² = ( a + b )² - 2ab

= [ { ( A + B )² - 2AB } / ( AB )² ] + 2( AB )³

= [ { ( - 4 )² - 2( - 1 ) } / ( - 1 )² ] + 2( - 1 )³

= [ 16 + 2 ] / ( 1 ) - 2( 1 )

= 18 - 2

= 16

3) Difference between roots of a quadratic equation :

= [ { - b + √( b² - 4ac ) } / 2a ] - [ { - b - √( b² - 4ac ) } / 2a ]

= [ - b + √( b² - 4ac ) + b + √( b² - 4ac ) ] / 2a

= [ 2√b^2 - 4ac ] / 2a

= { √b^2 - 4ac } / a

Thus,

= A² - B²

= ( A + B )( A - B )

= ( - 4 )( √{ 4² - 4( - 1 ) } / 1 )

= - 4 ( √( 16 + 4 ) )

= - 4√20

Hope it helped !!